FWI With Areal And Point Sources

ABSTRACT

A method, including performing, with a computer, up/down separation of geophysical data, which produces an approximate up-going wavefield and an approximate down-going wavefield; creating an areal source based at least in part on the down-going wavefield; and performing, with a computer, a full wavefield inversion process with the areal source, and an objective function measuring a misfit between modeled up-going wavefields and recorded up-going wavefields, wherein the full wavefield inversion process generates a final subsurface physical property model.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication 62/327,752 filed Apr. 26, 2016 entitled FWI WITH AREAL ANDPOINT SOURCES, the entirety of which is incorporated by referenceherein.

FIELD OF THE INVENTION

Exemplary embodiments described herein pertain generally to the field ofgeophysical prospecting, and more particularly to geophysical dataprocessing. Exemplary embodiments can infer properties of the subsurfacebased on information contained in geophysical data acquired in fieldexperiments.

BACKGROUND

This section is intended to introduce various aspects of the art, whichmay be associated with exemplary embodiments of the present invention.This discussion is believed to assist in providing a framework tofacilitate a better understanding of particular aspects of the presentinvention. Accordingly, it should be understood that this section shouldbe read in this light, and not necessarily as admissions of prior art.

Seismic inversion is a process of extracting information about thesubsurface from data measured at the surface of the Earth during aseismic acquisition survey. In a typical seismic survey, seismic wavesare generated by a source 101 positioned at a desired location. As thesource generated waves propagate through the subsurface, some of theenergy reflects from subsurface interfaces 105, 107, and 109 and travelsback to the surface 111, where it is recorded by the receivers 103. Theseismic waves 113 and 115 that have been reflected in the subsurfaceonly once before reaching the recording devices are called primaryreflections. In contrast, multiple reflections 117 are the seismic wavesthat have reflected multiple times along their travel path back to thesurface (dashed lines in FIG. 1). Surface-related multiple reflectionsare the waves that have reflected multiple times and incorporate thesurface of the Earth or the water surface (more generally, this is aninterface with air, which may be a water-air interface in the case ofmarine data or land-air interface in the case of land data) in theirtravel path before being recorded.

During seismic, electromagnetic, or a similar survey of a subterraneanregion, geophysical data are acquired typically by positioning a sourceat a chosen shot location, and measuring seismic, electromagnetic, oranother type of back-scattered energy generated by the source usingreceivers placed at selected locations. The measured reflections arereferred to as a single “shot record”. Many shot records are measuredduring a survey by moving the source and receivers to differentlocations and repeating the aforementioned process. The survey can thenbe used to perform Inversion, e.g., Full Waveform/Wavefield Inversion(FWI) in the case of seismic data, which uses information contained inthe shot records to determine physical properties of the subterraneanregion (e.g., speed of sound in the medium, density distribution,resistivity, etc. . . . ). Inversion is an iterative process, eachiteration comprising the steps of forward modeling to create simulated(model) data and objective function computation to measure thesimilarity between simulated and field data. Physical properties of thesubsurface are adjusted at each iteration to ensure progressively betteragreement between simulated and field data.

FWI is a seismic method capable of utilizing the full seismic record,including the seismic events that are treated as “noise” by standardinversion algorithms. The goal of FWI is to build a realistic subsurfacemodel by minimizing the misfit between the recorded seismic data andsynthetic (or modeled) data obtained via numerical simulation.

FWI is a computer-implemented geophysical method that is used to invertfor subsurface properties such as velocity or acoustic impedance. Thecrux of any FWI algorithm can be described as follows: using a startingsubsurface physical property model, synthetic seismic data aregenerated, i.e. modeled or simulated, by solving the wave equation usinga numerical scheme (e.g., finite-difference, finite-element etc.). Theterm velocity model or physical property model as used herein refers toan array of numbers, typically a 3-D array, where each number, which maybe called a model parameter, is a value of velocity or another physicalproperty in a cell, where a subsurface region has been conceptuallydivided into discrete cells for computational purposes. The syntheticseismic data are compared with the field seismic data and using thedifference between the two, an error or objective function iscalculated. Using the objective function, a modified subsurface model isgenerated which is used to simulate a new set of synthetic seismic data.This new set of synthetic seismic data is compared with the field datato generate a new objective function. This process is repeated until theobjective function is satisfactorily minimized and the final subsurfacemodel is generated. A global or local optimization method is used tominimize the objective function and to update the subsurface model.

Because of the strong nonlinearity inherent in the FWI method, theresults often depend on the quality of the starting velocity model.Choosing a poor starting model leads to the well-known phenomenon of“cycle-skipping” (when the traveltime difference between eventssimulated numerically in the computer and those acquired in the fieldexceeds half the period corresponding to the dominant frequency of thedata) and results in the optimization process converging to anundesirable local minimum. A significant contributing factor is theaccumulation of error as events are simulated using an inaccurate modelof the subsurface. This error is especially large for the so-calledmultiple reflections, which travel down to the subsurface and then backto the acquisition surface, where they get reflected down and repeatedlypropagate through the subsurface region, being recorded each time theyreach the surface where receivers are located. As an example, if due tomodel inaccuracies a primary event was simulated with a traveltime errorof Δt, then the corresponding first-order multiple would be simulatedwith an error of 2Δt, the second-order multiple would have an error of3Δt, etc. . . .

Unfortunately, correct modeling of multiples is challenging because evensmall inaccuracies in the background velocity model or mispositioning ofthe multiple-generating horizons can lead to significant accumulation oftraveltime errors as multiples repeatedly traverse the subsurface.

Ideally, one would like to turn this sensitivity of multiples to theinaccuracy of the model into an advantage by converting the traveltimeand amplitude errors into a source of information about the subsurfaceto be used in FWI.

One way to overcome the issue of error accumulation is to modelmultiples differently. Instead of performing numerical simulation usinga point source and a free surface boundary condition, one can injectrecorded field data traces as sources at receiver locations (Amundsenand Robertsson, 2014) and let the resulting wavefield propagate throughthe subsurface one more time. This spatially distributed source derivedfrom field data will be called “areal” source hereafter. If an absorbingboundary condition is used instead of the free surface one and thedirect arrival (from the source to receivers) is muted out, thenprimaries in the recorded field data will be converted into first-ordermultiples, first-order multiples will be converted into second-ordermultiples, etc. . . . Also note that, if the direct arrival is not mutedout, it will be converted into primaries (perhaps with a phase error,depending on implementation).

Because field data does not have any numerical traveltime errorsembedded in it and is propagated through the subsurface just once thanksto the absorbing boundary condition, no accumulation of errors occursand, using the notation introduced in the first paragraph above, thetraveltime error for all orders of multiples will be bounded by Δt. Thisapproach is well-known and has been used most recently in the FWIcontext by Zhang et al. (2013), although they did not point out thisparticular advantage of the method. Moreover, their proposed inversionmethod required extracting multiples from the field data (e.g., usingSRME) so that FWI could be performed by comparing modeled multiples withthose extracted from the field data.

A better approach would be to avoid the need to estimate multiplesseparately and perform FWI by using all recorded events, both primariesand multiples. This, in turn, necessitates modeling primaries andmultiples at the same time. In a recent publication, Tu and Herrmann(2014) proposed injecting a point source at the physical source locationtogether with an areal source (and an absorbing boundary condition) tomodel primaries and multiples at the same time for the purposes ofimaging (also known as migration or linearized inversion). Theypropagate the two source functions through a smooth medium, as is commonin imaging, and then correlate the resulting wavefield with theback-propagated data in order to obtain the subsurface reflectivity. Astheir paper points out, a disadvantage of this approach is thegeneration of “cross-talk” when multiples of different orders happen tocorrelate with each other, thus producing “fake” undesirable events.

SUMMARY

A method, including: performing, with a computer, up/down separation ofgeophysical data, which produces an approximate up-going wavefield andan approximate down-going wavefield; creating an areal source based atleast in part on the down-going wavefield; and performing, with acomputer, a full wavefield inversion process with the areal source, andan objective function measuring a misfit between modeled up-goingwavefields and recorded up-going wavefields, wherein the full wavefieldinversion process generates a final subsurface physical property modelfor hydrocarbon exploration.

In the method, the creating the areal source can include: performing,with a computer, a first simulation using a point source injected as amonopole into a starting physical property model with at least onesubsurface reflector and a free surface boundary condition imposed,wherein the performing the up/down separation is performed on datagenerated from the first simulation; performing, with a computer, asecond simulation using the point source, but with the point sourceinjected into the starting physical property model as a dipole with anabsorbing boundary condition; performing, with a computer, a thirdsimulation using an areal source including a down-going wavefieldobtained from the up/down separation, and an absorbing boundarycondition; adjusting simulated data from the third simulation and thesecond simulation to match their counterparts from the up/downseparation; and applying an adjustment derived from the adjusting of thesimulated data to the areal source and forming a hybrid source byconcatenating the adjusted areal source and the point source.

In the method, the adjusting can include using a shaping filter.

In the method, the shaping filter can be spatially varying, and themethod further can further include iteratively repeating a shapingprocess, wherein the shaping filter is iteratively changed during eachsubsequent iteration so that the shaping filter converges towards anidentity operator.

In the method, the shaping filter can be iteratively changed during eachsubsequent iteration in order to progressively improve the match betweenthe simulated data from the third simulation and the second simulationand their counterparts from the up/down separation.

In the method, the full wavefield inversion process can be a two stageprocess, a first stage including running full wavefield inversion usingobserved data as a source function to obtain an intermediate subsurfacephysical property model, and a second stage including running fullwavefield inversion using a point source as a source function with theintermediate subsurface physical property model being inverted to createa starting model for the second stage.

The method can further include independently adjusting the areal sourcerelative to the point source.

In the method, the performing the third simulation can include muting orsubtracting a direct arrival before the areal source is injected.

In the method, the performing the wavefield inversion process caninclude using an absorbing boundary condition.

The method can include drilling a well based at a location determined atleast in part from the final subsurface physical property model.

The method can include exploring for hydrocarbons using the finalsubsurface physical property model.

The method can include activating sources at or near Earth's surface ora water body surface, and recording reflected signals from the Earth'ssubsurface.

In the method, the areal source can be a hybrid source.

In the method, the areal source can be a non-hybrid source.

In the method, the geophysical data can be land data.

In the method, the geophysical data can be marine data.

The method can further include performing, with a computer, a fourthsimulation using a model consisting of the water layer to determine adirect arrival from the areal source; and subtracting the direct arrivalfrom a simulated wavefield generated by the third simulation.

BRIEF DESCRIPTION OF THE DRAWINGS

While the present disclosure is susceptible to various modifications andalternative forms, specific example embodiments thereof have been shownin the drawings and are herein described in detail. It should beunderstood, however, that the description herein of specific exampleembodiments is not intended to limit the disclosure to the particularforms disclosed herein, but on the contrary, this disclosure is to coverall modifications and equivalents as defined by the appended claims. Itshould also be understood that the drawings are not necessarily toscale, emphasis instead being placed upon clearly illustratingprinciples of exemplary embodiments of the present invention. Moreover,certain dimensions may be exaggerated to help visually convey suchprinciples.

FIG. 1 is an example of primary reflections and multiple reflections.

FIG. 2 is an exemplary flow chart illustrating an embodiment of thepresent technological advancement.

FIG. 3A illustrates an exemplary velocity model with alternating highand low velocity layers.

FIG. 3B illustrates a difference between a starting velocity model andthe true velocity model (FIG. 3A).

FIG. 4A illustrates an exemplary updated direction using a conventionaltechnique.

FIG. 4B illustrates an exemplary updated direction using the presenttechnological advancement.

FIG. 5A illustrates an exemplary propagation of a point source through avelocity model.

FIG. 5B illustrates an exemplary propagation of recorded data (i.e.,FIG. 3A) through the same velocity model.

FIG. 5C illustrates an exemplary propagation of the data in FIG. 3Athrough a different velocity model.

FIG. 6A illustrates an example of a true velocity model for a 2Dsynthetic example.

FIG. 6B illustrates an example of an initial velocity model for FWI.

FIG. 7A illustrates an example of conventional FWI using a point sourceas the source function.

FIG. 7B illustrates an example of FWI using the observed data as thesource function.

FIG. 7C illustrates an example of a two-stage FWI.

FIG. 8 is an exemplary flow chart illustrating an embodiment of thepresent technological advancement.

DETAILED DESCRIPTION

Exemplary embodiments are described herein. However, to the extent thatthe following description is specific to a particular, this is intendedto be for exemplary purposes only and simply provides a description ofthe exemplary embodiments. Accordingly, the invention is not limited tothe specific embodiments described below, but rather, it includes allalternatives, modifications, and equivalents falling within the truespirit and scope of the appended claims.

The present technological advancement can combine the simultaneous useof the point and areal sources (which we will call a hybrid source) withnonlinear inversion (FWI). The areal source is responsible for modelingmultiples. The point source is responsible for modeling primaries. Theadvantages over previously published work include using informationcontained in both primaries and multiples to update the model of thesubsurface and limiting the kinematic errors (thus reducing thecycle-skipping and making inversion less sensitive to the startingmodel). Because the areal source typically provides much widerillumination of the subsurface, it may be feasible to perform FWI usinga reduced subset of shot records, thus leading to a significant speedup. Additionally, because the subsurface model is iteratively updated inthe course of FWI iterations, thus leading to a gradual decrease of theresidual wavefield (the mismatch between the simulated and the acquireddata), the undesirable cross-talk observed by Tu and Hermann (2014) inimaging is expected to present a much smaller problem.

The present technological advancement will be described primarily in thecontext of Full Wavefield Inversion (FWI) of seismic data, but can beapplied to inversions of other types of geophysical data.

There are various well-known ways to inject an areal source in order tosimulate multiples. Equations 1-3 in Amundsen and Robertsson (2014)provide a recipe for doing this (in the case when a second-orderformulation of the wave equation is used), but require the knowledge ofboth pressure and its vertical gradient (or, equivalently the verticalcomponent of particle velocity) at receiver locations. If the pressuregradient is not available (as is the case in conventionalsingle-component marine acquisition), only one of the terms (the onerelying on pressure recordings only) can be used, but the resultingwavefield may have incorrect phases and amplitudes and propagate in bothup- and down-going directions instead of the desired down-goingdirection only, necessitating mitigation steps described in the nextsection.

The solution of the second-order formulation of the wave equation isequivalent to the solution of the following system of first-orderpartial-differential equations:

${{\partial_{t}{p\left( {x,t} \right)}} - {{\rho (x)}{c^{2}(x)}{\nabla{\cdot {v\left( {x,t} \right)}}}}} = {\sum\limits_{i = 1}^{n}\; {{f_{i}(t)}{\delta \left( {x - x_{i}} \right)}}}$${{{{\rho (x)}{\partial_{t}{v\left( {x,t} \right)}}} - {\nabla{p\left( {x,t} \right)}}} = {\sum\limits_{i = 1}^{n}\; {{g_{i}(t)}{\delta \left( {x - x_{i}} \right)}}}},$

where x is the vector of spatial coordinates, t is time; p is pressure;v is the vector of particle velocities; ρ is density; c is the speed ofsound in the subsurface; x_(i), f_(i)(t), g_(i)(t) are the spatiallocations and time signatures (i.e., recorded data) of receivers; and nis the total number of elements (receivers) comprising the areal source.In this case, inserting an areal source into the first of the aboveequations will produce an effect similar to that of the monopole, whileinserting it into the second equation will produce an effect similar tothe dipole, using the terminology of Amundsen and Robertsson (2014).

Depending on the boundary conditions at the top of the model, it may bepreferable to insert the areal source either as a dipole or as amonopole. In what follows, the areal and the point sources are insertedas dipoles in combination with the absorbing boundary conditions.

More general formulations of the wave equation exist (e.g., thevisco-elastic wave equation) and source insertion may need to beperformed differently depending on the specific form of the waveequation chosen to perform simulations.

Hybrid Source

The use of the hybrid source poses unique challenges in FWI. Since FWIrelies on accurate modeling of amplitudes, the areal source and thebalance between the point source and the areal source need to be chosencarefully. FIG. 2 provides an exemplary method of using a hybrid sourcein FWI.

In step 201, a first simulation is performed using a chosen point source200 with a reflecting free surface boundary condition imposed. The pointsource 200 can be injected into the model as a monopole. The model usedin the simulation should contain at least one reflector, so thatmultiples are generated.

In step 202, the up- and down-going wavefields are obtained byperforming up/down separation or a simplified version of it. In step202, the up-down separation of synthetic data should be compatible withthe type of field data to be used in inversion. Thus, if amulticomponent streamer was used in field acquisition, providing directmeasurements of pressure and particle velocity (or, equivalently,pressure gradient), and the two components are used to perform theup/down wavefield separation, the same type of receiver and the sameseparation method should be used in synthetic simulations. If, on theother hand, conventional single-component data are acquired in thefield, one could approximate the up-going wavefield by setting it equalto the acquired field data and the down-going wavefield by setting itequal to the acquired field data multiplied by “−1” (to account for thereflection coefficient of the air-water interface.) Other approximateup/down separation techniques, e.g., deghosting, can be used as well.

In step 203, a second simulation is performed using an areal source(including the down-going wavefield obtained in step 202) and anabsorbing boundary condition to generate up-going multiples. The secondsimulation can use the same model as in the first simulation. In step203, the direct arrival (i.e., the energy propagating in the waterdirectly from the source to the receiver) needs to be muted before theareal source is injected. The reason is that injecting the directarrival will generate a copy of the primaries (perhaps with an incorrectphase and amplitude, depending on implementation), thus duplicating thearrivals coming from the dipole source included in the hybrid source.

In step 204, the up-going multiples generated in step 203 are adjusted(e.g., filtered or scaled) to match their counterpart in step 202. Bymatch, ideally this can encompass equal, but more generally it refers tominimizing a misfit between the two in some norm (e.g., L2). In step204, the simulated wavefield from step 203 can contain both the up-goingmultiples and the direct arrival from the areal source. This directarrival needs to be subtracted off as it is not present in field data.Thus, an additional simulation, using a model comprising the water layeronly (for marine data, whereas land data would go through a near surfacemodel), can be performed and its result subtracted.

In step 205, the adjustment (e.g., shaping filter or a scalingcoefficient) derived in step 204 is applied to the areal source (thedown-going field data 206) and the direct arrival is muted orsubtracted. Examples of shaping filters or scaling coefficients can befound in Robinson, E. A., and Treitel, S., 1908, Geophysical signalanalysis, Prentice-Hall, Inc.

Furthermore, the up-going multiples modeled in step 204 may notrepresent a good match for multiples observed in field data due toerrors in modeling (e.g., incorrect position of the water bottom in themodel or insufficient sampling of field data which is used as an arealsource). When simulated and observed multiples do not match well,inverted models may suffer from artifacts, which typically manifestthemselves as false events in the model. In this case, an adjustment(e.g., a shaping filter) can be designed to improve the match betweenmodeled and observed multiples. This adjustment can then be applied tothe down-going wavefield used as the areal source. The ability to adjustthe point and areal sources independently is an additional degree offlexibility allowed by the use of a hybrid source, not present inconventional FWI, where both primaries and multiples are generated bythe same point source. If the adjustment (e.g., shaping filter) isspatially varying, then the shaping process can be repeated iterativelyuntil the adjustment becomes an identity operator (e.g., shaping filtersbecome band-limited delta-functions.) However, the shaping filter doesnot necessarily become an identity operator; rather the shaping filtercan be adjusted to converge toward the identity operator through apredetermined number of iterations or another stopping condition isreached. If the filter is spatially invariant, then only a singleiteration is required due to the linearity of the wave equation withrespect to time-domain shaping.

In step 207, a hybrid source is formed by combining the point source 200with the adjusted areal source from step 206. The point source is aseismic trace. The areal source is a collection of seismic traces. Thehybrid source can be formed by concatenating the areal source and thepoint source into a single file or using an equivalent method, the netresult being a simultaneous injection of both sources into thesimulation.

In step 208, FWI is performed using the hybrid source and an absorbingboundary condition on the surface, with all other aspects being exactlythe same as in the traditional approach of FWI. An objective functioncan be used to measure a misfit between modeled up-going wavefields andrecorded up-going wavefields, which generates an updated subsurfacephysical property model. While this example applies an absorbingboundary condition, a free surface condition could be used. However, thefree surface condition may be more sensitive to the velocity errorsbecause of the extra multiples.

EXAMPLES

The present technological advancement is further illustrated with anexample based on a simple layered velocity model. FIG. 3A illustrates anexemplary velocity model with alternating high and low velocity layers.FIG. 3B illustrates a difference between the starting velocity model(not shown) and the true velocity model (FIG. 3A), which is equal to 20m/s everywhere.

Accordingly, the FWI update direction is expected to indicate a velocityincrease everywhere in the subsurface. A numerical experiment isperformed using a single shot record with the source locationapproximately in the middle of the model (just below the free surface)and receivers extending both to the left and right of the sourcelocation up to 12 km away. The conventional approach produces an updatedirection (negative gradient), which indicates the desired velocityincrease only in the vicinity of the source location (FIG. 4A). Incontrast, the present technological advancement results in an updatedirection which has the correct sign almost everywhere (FIG. 4B).

Non-Hybrid Areal Source

Yet another alternative is to replace the hybrid source with an arealsource without muting out direct arrivals by using the fact that directarrivals will be converted into primaries after propagating through themedium one more time. As discussed previously, primaries will beconverted into first-order multiples, first-order multiples will beconverted into second-order multiples, etc. Therefore, if the medium isthe true medium, the data, after propagating it one more time, will be“equivalent” to the data itself This can be formally proved by using therepresentation theory by assuming infinite acquisition aperture andinjecting both pressure and vertical velocity data (Amundsen andRobertsson, 2014). In practice, however, this is not likely to happen,because seismic acquisition is always limited in nature; and forstreamer data, often only pressure data is recorded. However, it can beshown numerically that, by injecting only pressure data, we stillpreserve the travel time, although the amplitudes might not be accurateanymore. If the purpose is only to use the travel time information fromthe data to improve the velocity model, this modeling strategy can stillbe useful, especially when considering that it is less prone tocycle-skipping.

FIG. 5A shows simulated data obtained by propagating a point sourcethrough a velocity model, while FIG. 5B shows the simulated data whenusing the shot gather shown in FIG. 4A as the source and propagating itone more time through the same velocity model. Note that the travel timeinformation has been properly preserved. FIG. 5C shows the simulateddata when propagating the recorded data (FIG. 5A) through a differentvelocity model (one can think of it as an initial model for FWI). FIG.5C is massively different from FIG. 5B or FIG. 5A because a differentmodel, instead of the true model, was used for propagation. Thedifference between (b) and (c) shows the velocity sensitivity of such amodeling strategy, and the difference can be used in the FWI process toupdate the velocity model so that FIG. 5C can be closer to FIG. 5A or5B. During areal-source FWI, the simulated data using the areal sourceon the initial model (e.g. FIG. 5C) will be used to compare with theobserved data (e.g. FIG. 5A). The difference between the two is referredto as a residual, and the residual can be converted into a model updatesuch that once the model is updated, the difference (or residual)between the simulated and observed data will decrease. If convergencehas been achieved, the difference between the simulated data using anareal source on the final inverted model (e.g. FIG. 5B) and the observeddata (e.g. FIG. 5A) will achieve a minimum.

FIGS. 6A, 6B, 7A, 7B, and 7C present a numerical example of thenon-hybrid areal source method. FIG. 6A illustrates a true velocitymodel for a 2D synthetic examples, and FIG. 6B illustrates an example ofthe initial velocity model for FWI.

FIG. 7A illustrates the resulting model from conventional FWI using apoint source as the source function. FIG. 7B illustrates the resultingmodel from FWI using the observed data as the source function. FIG. 7Cillustrates the resulting model through a two-stage FWI process, whereinstage one includes running FWI using the observed data as the sourcefunction, and stage two includes running FWI using a point source as thesource function with the stage one inverted model as the starting model.

While conventional FWI (FIG. 7A) struggles to recover the rugose top ofsalt due to the negative impact of surface related multiples, the arealsource FWI (FIGS. 7B and 7C) does a much better job in delineating thetop of salt.

FIG. 8 illustrates a method of using a multi-stage FWI process with anon-hybrid areal source. Step 801 includes performing up/down separationof seismic data, which produces an approximate up-going wavefield and anapproximate down-going wavefield. Step 802 includes creating an arealsource based at least in part on the down-going wavefield. Steps 803 and804 constitute a multi-stage full wavefield inversion process. The firststage step 803 can include running full wavefield inversion usingobserved data (i.e., down going field data) as a source function toobtain an intermediate subsurface physical property model, and thesecond stage 804 can include running full wavefield inversion using apoint source as a source function with the intermediate subsurfacephysical property model being inverted to create a starting model forthe second stage.

Hydrocarbons can be managed according to the output subsurface modelgenerated by the methods of FIGS. 2 and 8. As used herein, hydrocarbonmanagement includes hydrocarbon extraction, hydrocarbon production,hydrocarbon exploration, identifying potential hydrocarbon resources,identifying well locations, determining well injection and/or extractionrates, identifying reservoir connectivity, acquiring, disposing ofand/or abandoning hydrocarbon resources, reviewing prior hydrocarbonmanagement decisions, and any other hydrocarbon-related acts oractivities.

While the exemplary embodiments discussed here pertain to marine data,the present technological advancement is applicable to land data.

In all practical applications, the present technological advancementmust be used in conjunction with a computer, programmed in accordancewith the disclosures herein. Any step in any of the methods discussedherein can be implemented with a computer. Preferably, in order toefficiently perform FWI, the computer is a high performance computer(HPC), known as to those skilled in the art, Such high performancecomputers typically involve clusters of nodes, each node having multipleCPU's and computer memory that allow parallel computation. The modelsmay be visualized and edited using any interactive visualizationprograms and associated hardware, such as monitors and projectors. Thearchitecture of system may vary and may be composed of any number ofsuitable hardware structures capable of executing logical operations anddisplaying the output according to the present technologicaladvancement. Those of ordinary skill in the art are aware of suitablesupercomputers available from Cray or IBM.

The present techniques may be susceptible to various modifications andalternative forms, and the examples discussed above have been shown onlyby way of example. However, the present techniques are not intended tobe limited to the particular examples disclosed herein. Indeed, thepresent techniques include all alternatives, modifications, andequivalents falling within the spirit and scope of the appended claims.

REFERENCES

The following references are hereby incorporated by reference in theirentirety:

-   Amundsen, L. and J. O. A. Robertsson, Wave equation processing using    finite-difference propagators, Part 1: Wavefield dissection and    imaging of marine multicomponent seismic data, Geophysics 79(6),    2014, pp. T287-T300;-   Tu, N. and Herrmann, F. J., Fast Imaging with surface-related    multiples by sparse inversion, Geophysical Journal    International (2015) 201, 304-31; and-   Zhang, D., W, Dai, and G. T. Schuster, Multiples Waveform inversion,    75th EAGE Annual Meeting, 2013.

What is claimed is:
 1. A method, comprising: performing, with acomputer, up/down separation of geophysical data, which produces anapproximate up-going wavefield and an approximate down-going wavefield;creating an areal source based at least in part on the down-goingwavefield; and performing, with a computer, a full wavefield inversionprocess with the areal source, and an objective function measuring amisfit between modeled up-going wavefields and recorded up-goingwavefields, wherein the full wavefield inversion process generates afinal subsurface physical property model for hydrocarbon exploration. 2.The method of claim 1, wherein the creating the areal source comprises:performing, with a computer, a first simulation using a point sourceinjected as a monopole into a starting physical property model with atleast one subsurface reflector and a free surface boundary conditionimposed, wherein the performing the up/down separation is performed ondata generated from the first simulation; performing, with a computer, asecond simulation using the point source, but with the point sourceinjected into the starting physical property model as a dipole with anabsorbing boundary condition; performing, with a computer, a thirdsimulation using an areal source including a down-going wavefieldobtained from the up/down separation, and an absorbing boundarycondition; adjusting simulated data from the third simulation and thesecond simulation to match their counterparts from the up/downseparation; and applying an adjustment derived from the adjusting of thesimulated data to the areal source and forming a hybrid source byconcatenating the adjusted areal source and the point source.
 3. Themethod of claim 2, wherein the adjusting includes using a shapingfilter.
 4. The method of claim 3, wherein the shaping filter isspatially varying, and the method further comprises iterativelyrepeating a shaping process, wherein the shaping filter is iterativelychanged during each subsequent iteration so that the shaping filterconverges towards an identity operator.
 5. The method of claim 4,wherein the shaping filter is iteratively changed during each subsequentiteration in order to progressively improve the match between thesimulated data from the third simulation and the second simulation andtheir counterparts from the up/down separation.
 6. The method of claim1, wherein the full wavefield inversion process is a two stage process,a first stage including running full wavefield inversion using observeddata as a source function to obtain an intermediate subsurface physicalproperty model, and a second stage including running full wavefieldinversion using a point source as a source function with theintermediate subsurface physical property model being inverted to createa starting model for the second stage.
 7. The method of claim 2, furthercomprising independently adjusting the areal source relative to thepoint source.
 8. The method of claim 2, wherein the performing the thirdsimulation includes muting or subtracting a direct arrival before theareal source is injected.
 9. The method of claim 1, wherein theperforming the wavefield inversion process includes using an absorbingboundary condition.
 10. The method of claim 1, further comprisingdrilling a well based at a location determined at least in part from thefinal subsurface physical property model.
 11. The method of claim 1,further comprising exploring for hydrocarbons using the final subsurfacephysical property model.
 12. The method of claim 1, further comprisingactivating sources at or near Earth's surface or a water body surface,and recording reflected signals from the Earth's subsurface.
 13. Themethod of claim 1, wherein the areal source is a hybrid source.
 14. Themethod of claim 1, wherein the areal source is a non-hybrid source. 15.The method of claim 1, wherein the geophysical data is land data. 16.The method of claim 1, wherein the geophysical data is marine data. 17.The method of claim 2, wherein the method further comprises: performing,with a computer, a fourth simulation using a model consisting of thewater layer to determine a direct arrival from the areal source; andsubtracting the direct arrival from a simulated wavefield generated bythe third simulation.